Question

Out of four numbers whose average is 75, the first number is one-fourth of the sum of the last three numbers. The first number is:

• A. 52
• B. 56
• C. 60
• D. 64

Hint:

In such problems, use the average formula and break down the relationships between the numbers to simplify the solution.

Answer 1

The Correct Option is C

Let the four numbers be \( a, b, c, d \). We are told that the average of these numbers is 75, so: \[ \frac{a + b + c + d}{4} = 75 \quad \Rightarrow \quad a + b + c + d = 300. \] Also, \( a = \frac{1}{4}(b + c + d) \). Substitute this into the sum equation: \[ \frac{1}{4}(b + c + d) + b + c + d = 300 \quad \Rightarrow \quad \frac{1}{4}(b + c + d) + (b + c + d) = 300. \] Simplifying, we get: \[ \frac{5}{4}(b + c + d) = 300 \quad \Rightarrow \quad b + c + d = 240. \] Thus, \[ a = \frac{1}{4} \times 240 = 60. \] So, the first number is 60, which corresponds to option (C).